Perimeter of a Polygon

Polygon is a geometric bounded shape comprising a number of line segments which is finite. The sides of polygon's segments are called edges while the point at which the two edges meet each other to form the vertices. It is a plane or two-dimensional figure.  A polygon is named after the number of sides it has. Thus, we have the triangle with three sides, a pentagon with five sides and n-gon for a polygon with an n number of sides. The perimeter, on the other hand, is a 1-D measure which calculates the length of the path surrounding a plane figure.


Properties of a Polygon:

The polygon has the following properties:

  • It is a figure which is closed.

  • Polygons are 2-D shapes.

  • The sides of polygons do not cross each other.

  • At every vertex, only two sides meet.

  • Regular polygons have all angles and sides equal.

  • Convex polygons comprise interior angles of less than 180 degrees.

  • Concave polygons have at least one angle which is more than 180 degree.


How to Find the Perimeter of a Polygon?

Perimeter refers to the sum of lengths of sides of a polygon. Perimeter of regular polygon formula is:


Perimeter= N. S units.


Where N is the number of sides that a polygon has and S refers to the side’s length.

The different types of polygon and the perimeter of the polygon formula for each case are as follows:


Perimeter of a Triangle:

To calculate the perimeter of a triangle, we first need to take into account what kind of triangle we are dealing with. Nevertheless, the perimeter of a triangle remains the sum of the length of its sides. Triangle is a form of a polygon with three sides or as the name suggests three angles. The perimeter of a triangle formula is given below:


Perimeter of Isosceles Triangle:

An isosceles triangle is a form of a triangle with two equal angles and sides. The perimeter of an isosceles triangle the sum of the three sides. If A and B and C are the vertices and AB and BC are the equal sides then the perimeter can be written as 2AB+AC.


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Perimeter of Equilateral Triangle:

The equilateral triangle consists of three equal sides and each angle measures 60 degrees. If A and B and C are three vertices then the perimeter of equilateral triangle= 3AB=3BC=3AC.


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Perimeter of a Rectangle:

A rectangle is a form of quadrilateral (or comprising 4 sides). The rectangle has four angles and four corners. Each angle of the rectangle measures 90 degrees and it has the opposite sides equal but adjacent sides unequal. The perimeter of a rectangle is the sum of the lengths of its sides.


The perimeter of a rectangle formula is 2( A + B) where A is the length and B is the breadth of the rectangle.


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Perimeter of a Square:

A square is also like the rectangle a quadrilateral (figure having four sides). The square too has each angle measuring 90 degree and the diagonals are equal. However, unlike the rectangle all the sides of the square are equal. Thus, a rectangle can be called a rectangle whose adjacent sides are equal. The perimeter of a square formula is 4*S where S is the length of the side of the square.


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Did you Know?

The word polygon comes from the Greek term ‘poly’ which stands for ‘many’ and ‘gonia’ which means angle. A polygon whose sides are unequal is known as irregular. Every interior angle in a polygon is always less than 180 degrees. A polygon with nine sides is termed nonagon. All Bah’I Temples are built as nonagons. Such polygons are readily used in architecture and are common in everyday life.


Solved Examples:

1) Jyoti goes for a walk on a path around a rectangular park. The park has length 20 m and breadth 45 m. What is the total distance that she travels?


Ans) The figure we have is a rectangle. The perimeter formula of the rectangle is 2( A+B). Here A= 20m and B=45m. Thus perimeter would be 2(45+20)= 130m.

Thus, the total length travelled by Jyoti is 130m.


2) A triangle has all angles measuring 60 degrees. One of the sides of the triangle is 30m. What is the perimeter of the triangle?


Ans) Since all the angles in the triangle are 60 degrees, it is an equilateral triangle. Thus, the perimeter of an equilateral triangle is 3*L. Here we have L=30 m. Thus perimeter= 3.30=90m. Hence, the perimeter is 90 m.


3) An isosceles triangle has a perimeter of 40 cm and base 16 cm. Each of the two sides have a length of measure____


Ans) The isosceles triangle has two sides which are equal. It’s perimeter=2AB+BC. Hence, its equal sides are 40 - 16 = 24. Thus, each of the two equal sides would have a length of 24/2=12cm.

FAQ (Frequently Asked Questions)

1) How do you Find the Perimeter of a Polygon with n Sides?

Ans) In general perimeter is just the sum of the length of the sides comprising a figure. A polygon is no exception to this. Thus, if the polygon has 5 sides then the sum of those five sides would give us the required perimeter. For a regular polygon, the process is much simpler because a regular polygon is both equiangular and equilateral. In other words, all the sides of an equilateral polygon are equal and all the angles in the polygon are equal as well. Thus, the perimeter would only be the number of sides multiplied by the length of each side.

2) How to Find the Perimeter of a Square Whose Sides are not Given but Diagonal is 16 m?

Ans) In this question, the diagonal of the square is known to us. We also know the adjacent sides of a square are at right angles. The Pythagoras theorem states that the sum of squares of the base and height of a right-angled triangle is equal to the hypotenuse. This property can be effectively used in this theorem since diagonal splits the figure into two right-angled triangles. Hence, if ‘d’ is diagonal and ‘a’ is the side, then we easily find out the solution with the help of the formula: a2 + a2 =d2.

Or, 2a2=d2

Or, 2a2 = 162

Or, 2a2 = 256

Or, a2 = 128

Or, a=11.31

Perimeter would be 11.31*4 = 45.24 m.